We present a nondeterministic model of computation based on reversing edge
directions in weighted directed graphs with minimum in-flow constraints on
vertices. Deciding whether this simple graph model can be manipulated in
order to reverse the direction of a particular edge is shown to be
PSPACE-complete by a reduction from Quantified Boolean Formulas. We prove
this result in a variety of special cases including planar graphs and highly
restricted vertex configurations, some of which correspond to a kind of
passive constraint logic. Our framework is inspired by (and indeed a
generalization of) the “Generalized Rush Hour Logic” developed by
Flake and Baum [4].

We illustrate the importance of our model of computation by giving simple
reductions to show that multiple motion-planning problems are PSPACE-hard.
Our main result along these lines is that classic unrestricted sliding-block
puzzles are PSPACE-hard, even if the pieces are restricted to be all dominoes
(1 × 2 blocks) and the goal is simply to move a particular
piece. No prior complexity results were known about these puzzles. This
result can be seen as a strengthening of the existing result that the
restricted Rush HourTM puzzles are PSPACE-complete [4], of
which we also give a simpler proof. We also greatly strengthen the conditions
for the PSPACE-hardness of the Warehouseman's Problem [6], a classic
motion-planning problem. Finally, we strengthen the existing result that the
pushing-blocks puzzle Sokoban is PSPACE-complete [2], by showing that it
is PSPACE-complete even if no barriers are allowed.